Cremona's table of elliptic curves

1424 = 2⁴ · 89

Field	Data	Notes
Atkin-Lehner	2- 89+	Signs for the Atkin-Lehner involutions
Class	1424c	Isogeny class
Conductor	1424	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-1493172224 = -1 · 224 · 89	Discriminant
Eigenvalues	2- -1  3  4  6  2  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,96,1792]	[a1,a2,a3,a4,a6]
j	23639903/364544	j-invariant
L	2.2437919932669	L(r)(E,1)/r!
Ω	1.1218959966334	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	178a1 5696i1 12816m1 35600r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1424c1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-1	3	4	6	2	3	-5	3	0	-5	-10	0	1	-12	9	-12	-10	4	6	-1	10	12	+	17

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Quadratic twists for elliptic curve 1424c1

-4	8	-3	5	-7	89
178a1	5696i1	12816m1	35600r1	69776y1	126736d1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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